This walkthrough will more or less cover the bosses, along with some tips on builds. All of these will allow you to beat the game on single-player, without using consumables.
Boss 1: There's really not much to this fight. It's generally pretty safe to stay near the center; feel free to dodge to the left and the right as needed. The boss won't really get harder or anything, so it's pretty easy. Note that the bolts on the side kind of move faster than the bolts in the center, so staying reasonably centered is a good idea.
Boss 2: It has two attacks: aimed columns of purple balls and a shotgun barrage, both from the nostrils. You can shoot either the nose or the eyes. On easier difficulties, you can walk through the shotgun relatively easily. On higher difficulties, it's generally easier to stand near one of the eyes. There's a somewhat safe spot at about a 45 degree angle from the nostrils and directly under an eye where you only have to dodge a small amount of fire(you'll need to move around a little). For insane, it's probably easiest to go a little glassy(see below).
Boss 3: This one is built for endurance. It spits webs(which last forever) and summons bugs from the bottom of the screen. If it eats a bug, then it gets full health. The key is actually to focus on attacking the boss, and not to go after the bugs prematurely. When the spider goes after the bugs, shoot the bugs and deny the spider the meal. As a bonus, the spider stops firing when it eats. Going for a glassy build is probably the best way to win, as the webs do pile up. Webs will slow you to a crawl, but it's still slightly possible to avoid shots by continuously moving in one direction.
Boss 4: This guy has 3 attacks: the expanding circles, the V shaped attack, and the lines of fire. It also has the ability to summon drones(including a med drone), but those don't tend to be much of a threat. The medical drone won't heal much, so you can kind of ignore it if there's a firestorm. The expanding circles is by far the easiest to beat: simply move up 1/4 length of the screen or so, and all will pass by. For the lines of fire, try your best to stay between the lanes of fire. The V is rather difficult to dodge. It's almost certainly a victory if the boss leads with expanding circles, since you'll have a lot of time to deal damage for free.
Boss 5: It's invulnerable as long as its shield is up, but any of the red beetles exploding near it will take down the shield. There's a lot of red beetles, so it's generally vulnerable. If you stay at the top of the screen, you'll be generally safe. If you're feeling particularly cowardly, you can use melee drones to take it down. Note that the red shield doesn't block projectiles that are not headed for the boss, so you can shoot a beetle that's to the back and side of the boss.
Boss 6: The Yeti can be a brutal boss. It chucks indestructible ice walls and pounds tons of shots out. Thankfully, there's a cheap and easy strategy. If you observe carefully, no shots ever travel on the top left edge of the screen. So, you can simply stand there. If you're bored of watching drones take him down, you can actually move rightwards until your main shot hits his left fist, which will take him down rather quickly.
Boss 7: It has two attacks; A V-shaped attack and a more random spam. For the Vs, fly through the holes in the center; for the shot spam, the boss tends to leave holes in the center(so you'll essentially follow the boss, but time-delayed). If you can't make the holes in the Vs, you can also fly in through the sides, but this gets a little more risky/difficult. There's also soldiers; you don't have to pick them up, but they do help in point defense. My advice is to only go after the safe ones: you lose soldiers when you get hit, and you can always point defense by moving backwards a little, which brings the moths into your main field of fire.
Boss 8: It changes colors(red, green, yellow, blue) periodically, and can only be hurt if you grab a bubble with the same color. Attack-wise, it uses walls of red, hoses of red projectiles, and aimed blue shots. An endurance build is not a bad idea for this particular boss. Keep in mind it will change colors at the rate of twice/wall of bubbles. If you can't find the appropriate bubble, or the boss is about to change colors, it's probably a good idea to hold on to what you have. When attacking, dashing in from the side seems to be the best strategy, and running away if it gets difficult. Much like boss 5, if you stay near the top edge, you're mostly safe, except this time there's the blue aimed shots.
Addendum: It seems a lot of people hate this boss. There's 3 fire modes: blue, horizontal red, and red whips. In addition to the color control described above(anticipate color changes), here's some combat tips: It's very easy to attack the boss when he's using horizontal red projectiles, since all you need to do is strafe and stay out of field of fire. When the blue attacks go, traverse from left to right side of screen, which will give you some extra shots on boss. The whips are somewhat harder to dodge, but if you only get hit by them, you should do fine.
Boss 9: It'll seem like everything is so much tougher. The bugs are rather high hp(given the huge quantity). It may help to have ramming drones to defend against the swarm. Above all, dodge the fists. Keep moving, and quickly. Some fists may be aimed, I'm not completely sure. Being hit by a fist will deal ludicrous amounts of damage, so ignore the bugs. The fist will also squash the bugs, which helps quite a bit. Once he comes down to ground level, unleash whatever offense you have. Note: it is possible that the troll fist will insta-kill you on insane(300+ dmg).
Boss 10: Mecha-turtle. It has two attacks: some small energy pellets and a revolving blue maelstrom(of more pellets). The energy pellets aren't typically that bad, but if you find them difficult to dodge due to difficulty, move to the side, as there's plenty of opportunity to attack. Note that some energy pellets are aimed, so keep moving a little. When the blue maelstrom first starts, step through the front to get into the inner layer(just outside the second ring or so). It'll contract, so step out, then expand, so step back in, and then do so once more. It'll then spin for a while, but you'll be safe in the second layer safe zone or so. As it ends, step out via the 5:00 direction.
Boss 11: The goal is to lure the metal protector robot into the circular platforms on each side to lower the shields. Begin by moving to the left side of the screen, since that's where the guardian starts. Once you bring down the glass shields, attack the center guy. He'll aim for you with his center shot, so you'll need to jiggle between the left side and the right side, while maintaining fire. When the glass goes back up, run to the other side. It helps to stay near the top of the screen while baiting, I find. A shield drone or two might be helpful to pass through the center unscathed.
Edit: Apparently, you can get stuck in the platform with the guardian. You don't need to be very far up vertically, as it only tracks your horizontal position.
Boss 12: At the beginning, a shield sphere will drop. Don't pick it up(unless you have shield suit). It'll shoot red shots, which are somewhat difficult to avoid. If it gets too intense, you can generally survive a little better by staying to the side. After a while, it'll pop down, which is when you want to grab the shield to avoid being hit by the fire wave(does around 2x shot damage). If you manage to do so, you'll generally be able to win via pure tanking, especially if that's how you're built.
Note: Remember that being hit gives you temporary invulnerability, so you can avoid some damage by getting hit by the final shots if you grabbed the shield.
Boss 13: Mr. turbine is very aggressive, but relatively weak. If you go glassy, it's quite likely that you pound through him. The turbines aren't hugely dangerous, but avoiding stepping in them as you will be mostly unable to dodge. His most dangerous attack is his aimed columns of shots. These tend to arrive during his other shot attacks, so it may be very difficult to dodge. Overall, a glassy strategy will bring him down pretty quickly. You can find some moderate respite if you run to his sides.
Boss 14: Viral asteroidz! This one is kind of tricky, especially on insane. Having beam attack isn't a bad idea, or alternatively, try an endurance build. There's 5 forms: the first two are big but not very dangerous. The last two tend to crisp pretty easily. The most dangerous, then, is the middle form(x4). It fires very fast shots, which tend to hit you in the shot storm. My advice is to make sure that that form lasts the least amount of time, and crisp the little guys relatively quickly.
Edit: Alternate strategy, with some thanks to twilight2. The vertical ceiling is somewhat higher on this fight, so you can actually stay above the boss's projectiles. Only the smallest form can shoot upwards. Use melee drones to wear down the viruses to tier 4 or so, and when the little guys start popping up, swoop to the bottom of the screen and mow them down. Rely on the invulnerability from being hit to stay alive.
Boss 15: This guy's pretty easy. An endurance build is recommended, but not required. Your normal shots do some damage, but the majority of damage will come from tricking him into crashing into the rock(exclamation mark). Move out of the bird's way when it attacks, and tank/avoid the blue shots. Can be a great opportunity to take a break and heal. It'll take damage even if it's not charging, so long as the screen scrolls him into the rock.
Boss 16: The key is to keep him not too hurt(bar goes up), and not too unhurt(bar drops too much). If either happens, you'll be stunned. I strongly recommend 2 melee drones. These keep the rhythm almost perfectly, making your job very easy. Stand to one side and hammer him with the drones, swapping sides and letting off on the attack as needed.
Boss 17: The slime throws around a lot of purple stuff, and summons mini-slimes. The mini-slimes aren't a huge threat, but they aren't very hard to kill either. A glassy build works very well, but for the most part, remember that the purple stuff detonates behind you and won't really hurt you on the way in. Stay focused on dodging, as it has no other attacks.
Edit: According to the dev, the mini-slime eyes will allow the slime to aim at you after 3 seconds or so, so focus some firepower on killing them.
Boss 18: It throws a lot of firepower, most of it somewhat aimed. There's also a laser drone that flies around. Going glassy can save a lot of difficulty/dodging, but endurance should work too. When the laser beams activate, go around within the revolving beams. You'll have to expend some effort to chase down the boss a little, but overall, should be doable(maybe with a couple of tries).
Boss 19: You can move the platform by standing on the edges of it. Your first move should be to move the platform backwards, as you start way too close. This will buy you some reaction time. It'll alternate between a barrage of tightly aimed shots and a barrage of loosely aimed shots(moving a few pixels will dodge this). The loosely aimed shots are difficult to dodge, it's quite likely you'll be hit by at least one. if you're still using the insane glassy build, make sure it takes 3+ hits to kill you. If you only take one hit every time he rises, you should be able to win without too much trouble
Boss 20: It's all about beef here. The most dangerous part is the shots that are fired. I went with the medic build, I suppose a shield build could work but I didn't like it. Fire the cannons at the open eye, keeping in mind there's a charge time on each one. When the tentacles withdraw, grab the shield. Depending on how much you want to grind, go ahead and buy as many final tech armors and final tech protectors as you can. Tank your way through; it's mostly just endurance.
Note: after some more playthroughs, I recommend having at least 2 tech protectors first, as they help you reduce the damage substantially. I also recommend staying closer to the shield, and ignoring the open eyes unless if it's safe to attack. There's plenty of free time after the coast is clear to hit the eye, and it's more of an endurance match. I've beaten it with 1 tech protector + 3 armors on heal suit, but keep trying and buying more armors and protectors until you win.
Note 2: The kraken has been updated as described in the patch notes. It is now imperative for you to pick up shield drops, or the kraken will heal 35%. The same strategy ought to apply, however, though it should now also be possible to do this with a glassy build(I'm guessing half-glassy is a good choice).
Some helpful builds:
Glassy: Focus on RoF, lucky strike, and bullets which are cappable. Lucky strike will give doubled dmg shots, which is often worth more than the raw damage. Cleaner Wrist 2000 is a very good resource for this build. I don't personally like the raw damage upgrades(Ie +90 dmg); instead, picking something like +40 dmg + 40 hp is better. Fine-tune your builds so that you can take multiple hits. A medic suit is actually not a bad idea: it provides extra hp for cheap, and has good RoF. I recommend this build for most of insane, as it generally works with a few tweaks.
Endurance: At the beginning, try to maximize your heal. That will be about 5-7 hp per 20 seconds. Later, when the first medic suit comes out(after beating boss 9), you can use that, but it only heals 2 hp. Heal II heals 18, heal IV heals 72(dunno where heal III went), and heal V heals 90. Use the heal ability as often as you can, and get 50% cooldown(or near) for heals II+. After a while, the manual heal is worth more than the automatic heal, especially on insane.
I note that some people are saying that dancing fire is amazing - I don't really agree. It does a moderate amount of damage, and the fire is movable, but I'm extremely annoyed by the fact that your character stops firing/moving when you do so. This overall lowers dps(especially if you're glass), and provides relatively crappy invulnerability. It also sucks that the fire runs out.
Two players: don't, unless you have a second player or godlike ability to multitask. The devs have stated that it INCREASES boss damage and hp(by 30+%), so don't.
